Verify that |r^{t}(s)|=1.Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >.

Annette Arroyo 2020-10-28 Answered
Verify that rt(s)=1.Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >.
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Talisha
Answered 2020-10-29 Author has 93 answers
Given:The function r(t)= < 2 cos t, 2 sin t, t >Proofs:The curve in terms of arc length is,r(s)=2 cos (s5)i + 2 sin (s5)j + s5k.On differenting the vector-value function r(s), we getr(s)= 25 sin(s5)i + 25 cos(s5)j + 15kFrom this calcute r(s) asr(s)= (25 sin(s5))2 + (25 cos(s5))2 + (15)2
= 45 + 15
= 55
=1Hence, it is proved that r(s)=1
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